1. Surface Area of a Pyramid

2. If you split the triangle into 2, you can use Pythagoras…
Starter
Calculate the Area of these Triangles. You will need to think carefully on the second one…
If you split the triangle into 2, you can use Pythagoras…
6cm
6cm
7cm
8cm
5.196cm
3cm
6cm
base x height 2
c2 – b2 = a2
5cm
62 – 32 = a2
base x height 2
6 x
27 = a2
5 x 7 2
5.196… = a
= 17.5cm2
= 15.59cm2

3. Surface Area of a Pyramid
Today we are going to look at finding the Surface area of Pyramids
This will involve the use of Pythagoras’ Theorem like we saw in the starter
This topic is graded A/A* depending on the difficulty of the question!

4. Surface Area of a Pyramid
Find the Surface Area of this Pyramid
As all the lengths are the same, all sides are the same. Therefore all you need to do is find the area of one side, then multiply by 4
c2 – b2 = a2
Sub in c and b
82 – 42 = a2
8cm
8cm
Work out the left side
8cm
48 = a2
6.93cm
Square root
6.93… = a
4cm
8cm
base x height 2
Remember throughout this you should keep using the exact values in your calculator, rather than the rounded ones!
Sub in the base and height
8 x
Work out the sum
= 27.71cm2
Multiply by 4 as there are 4 sides
= cm2

5. Surface Area of a Pyramid
Find the Surface Area of this Pyramid
c2 – b2 = a2 7m
Sub in c and b 7m 7m
72 – 52 = a2
Work out the left side
24 = a2
4.9m
Square root
4.9 = a 5m
10m
10m
base x height 2
Sub in the base and height
10 x 4.9 2
Work out the sum
= 24.49m2
Multiply by 4 as there are 4 triangular sides
= 97.98m2
10 x 10 = 100m2
Don’t forget the base!
100m = m2

6. Summary We have recapped our knowledge of Pythagoras’ Theorem
We have looked at how to use this to work out the Surface Area of Pyramids